SOLUTION: Solve x^4-6x^2+24x-40=0

Question 1133832: Solve x^4-6x^2+24x-40=0
Answer by t0hierry(194) (Show Source): You can put this solution on YOUR website!
Solve x^4-6x^2+24x-40=0
x = 2
is a solution found by trial and error.
Then we write
(x-2)(x^3 + ax^2 + bx + c) = x^4 + ax^3 -2x^3 + bx^2 - 2a x^2 + cx-2 bx - 2c =
x^4 + (a-2)x^3 + (b-2a)x^2 + (c - 2b)x - 2c
a-2 = 0
b-2a = -6
c = 20
a = 2
b = -2
check: c -2b = 20 + 4 = 24
so:P(x) = (x-2)(x^3 -2 x^2 -2x -20)

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